算术层次中的学习理论
Learning Theory in the Arithmetic Hierarchy
摘要：
我们考虑了在不同的学习准则下可学习的一致可计算可积族的指数集的算术复杂性。我们确定这些集合的有限学习，学习的限制，行为正确的学习和异常学习的限制的标准概念的确切复杂性。在证明行为正确学习的$Σ_5^0$ -完备性结果中，我们证明了一个独立的结果;如果一个均匀可计算可枚举的家族是不可学习的，那么对于任何可计算的学习者，都有一个$Δ_2^0$枚举见证失败。
英文摘要：
We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning, learning in the limit, behaviorally correct learning and anomalous learning in the limit. In proving the $Σ_5^0$-completeness result for behaviorally correct learning we prove a result of independent interest; if a uniformly computably enumerable family is not learnable, then for any computable learner there is a $Δ_2^0$ enumeration witnessing failure.
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